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Research Article | Open Access

Derivative of self-intersection local time for the sub-bifractional Brownian motion

Nenghui Kuang1( ), Huantian Xie2
School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276005, China
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Abstract

Let S H , K = { S t H , K , t ≥ 0 } be the sub-bifractional Brownian motion (sbfBm) of dimension 1, with indices H ∈ ( 0 , 1 ) and K ∈ ( 0 , 1 ] . We mainly consider the existence of the self-intersection local time and its derivative for the sbfBm. Moreover, we prove its derivative is H o ¨ lder continuous in space variable and time variable, respectively.

Keywords

sub-bifractional Brownian motionself-intersection local timederivative of self-intersection local time
CLC number: 60G22, 60J55

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10286-10302
DOI: 10.3934/math.2022573

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Cite this article:
Kuang N, Xie H. Derivative of self-intersection local time for the sub-bifractional Brownian motion. AIMS Mathematics, 2022, 7(6): 10286-10302. https://doi.org/10.3934/math.2022573

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Received: 26 December 2021
Revised: 22 February 2022
Accepted: 02 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)